What gauge wire do I use

Everyone, thank you for all this advise. Since I am getting in deep on this, I have expanded the project slightly. The run remains at 200' (195' to be exact). I am thinking of doing this with thhn wire in conduit. I will run 6 gauge for trailer, an additional 10 gauge wire for a 20 amp outlet and a 6 gauge neutral wire. What gauge should my ground wire be? Should any of the wire gauges I mentioned above be altered? I am planning stranded copper. I'll price out the difference of this setup vs running 6/3 uf-b cable. Maybe I'm wastying my efforts and the uf-b cable would just be cheaper. Don't know. thinking outloud.

Thanks!